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Active walker models have recently proved their great value for describingthe formation of clusters, periodic patterns, and spiral waves as well as thedevelopment of rivers, dielectric breakdown patterns, and many otherstructures. It is shown that they also allow to simulate the formation of trailsystems by pedestrians and ants, yielding a better understanding of human andanimal behavior. A comparison with empirical material shows a good agreementbetween model and reality.  Our trail formation model includes an equation of motion, an equation forenvironmental changes, and an orientation relation. It contains some modelfunctions, which are specified according to the characteristics of theconsidered animals or pedestrians. Not only the kind of environmental changesdiffers: Whereas pedestrians leave footprints on the ground, ants producechemical markings for their orientation. Nevertheless, it is more importantthat pedestrians steer towards a certain destination, while ants usually findtheir food sources by chance, i.e. they reach their destination in a stochasticway. As a consequence, the typical structure of the evolving trail systemsdepends on the respective species. Some ant species produce a dendritic trailsystem, whereas pedestrians generate a minimal detour system.  The trail formation model can be used as a tool for the optimization ofpedestrian facilities: It allows urban planners to design convenient waysystems which actually meet the route choice habits of pedestrians.

Active walker model for the formation of human and animal trail systems